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Tamiku [17]
3 years ago
14

Simplify. cos^2[(pi/2) - x] + cos^2[(pi/2) - x] + cos^2x

Mathematics
1 answer:
Ipatiy [6.2K]3 years ago
5 0

Numerator
<span><span>cos<span>(<span>π/2</span>−x)</span></span>=<span>cos<span>(<span>π/2</span>)</span></span><span>cosx</span>+<span>sin<span>(<span>π/2</span>)</span></span><span>sinx</span></span>

now <span><span>cos<span>(<span>π/2</span>)</span></span>=0 and <span>sin<span>(<span>π/2</span>)</span></span>=1</span>

simplifies to : 0 + sinx = sinx

Denominator

<span><span>sin<span>(<span>π/2</span>−x)</span></span>=<span>sin<span>(<span>π/2</span>)</span></span><span>cosx</span>+<span>cos<span>(<span>π/2</span>)</span></span><span>sinx</span></span>

simplifies to : cosx + 0 = cosx

<span>⇒<span><span>cos<span>(<span>π/2</span>−x)</span></span><span>sin<span>(<span>π/2</span>−x)</span></span></span>=<span><span>sinx/</span><span>cosx</span></span>=<span>tan<span>x</span></span></span>

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Have a good day! : )

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4 0
3 years ago
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Mary wants to fill in a cylinder vase. At the flower store they told her that the vase should be filled 3/4 for the flowers to l
Nimfa-mama [501]

Answer: 376.98192 mL

Step-by-step explanation:

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note: also keep in mind that value of π is 3.141516

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8 0
4 years ago
Find the measure of the indicated angle to the nearest degree. Thanks.
Sholpan [36]

Answer:

θ ≈ 40°

Step-by-step explanation:

Since, sinθ = \frac{\text{Opposite side}}{\text{Hypotenuse}}

cosθ = \frac{\text{Adjacent side}}{\text{Hypotenuse}}

tanθ = \frac{\text{Opposite side}}{\text{Adjacent side}}

In the picture attached,

Measures of adjacent side and opposite side of the triangle have been given. Therefore, tangent rule will be applied in the given triangle.

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3 years ago
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USPshnik [31]

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